7. Crisis and Uncertainty

09/27/16 • 13 min

Adrian Moore’s series on philosophical thought on infinity finds him mired in a near meltdown in mathematics.

Adrian tells the story of the controversy caused by the work of the German mathematician, Georg Cantor, on the infinite. In a world of paradoxes, we meet the nun who can't decide whether to pray for herself. Her dilemma is beautifully explained by Marcus Giaquinto, Emeritus Professor of Philosophy at UCL, in conversation with Adrian.

And we find out how an associated paradox, first posed by one of the giants of 20th century philosophy, Bertrand Russell, devastated the career of another German mathematician and philosopher.

The arguments of the early 20th century no longer plague modern mathematics in the way that they did. As Adrian explains however, by subjecting the infinite to formal scrutiny, mathematicians have ended up confronting puzzles at the very heart of their discipline.

Producer: Philippa Goodrich

A Juniper production for BBC Radio 4, first broadcast in September 2016.

Adrian Moore’s series on philosophical thought on infinity finds him mired in a near meltdown in mathematics.

And we find out how an associated paradox, first posed by one of the giants of 20th century philosophy, Bertrand Russell, devastated the career of another German mathematician and philosopher.

Producer: Philippa Goodrich

A Juniper production for BBC Radio 4, first broadcast in September 2016.

Previous Episode

6. The Mathematics of the Infinitely Big

Adrian Moore continues his exploration of two and a half millennia of philosophical thought on infinity.

Discover the brilliant but tortured German mathematician, Georg Cantor, who devised a way of distinguishing between infinitely big numbers and of performing calculations with them.

His work was revolutionary but, as Adrian discovers, it greatly polarised opinion amongst his late 19th and early 20th century contemporaries.

We hear how Cantor himself suffered a complete breakdown in his mental health.

As Adrian takes us with him deep into the world of infinite set theory, he enlists the help of Mary Leng, Senior Lecturer in Philosophy at York University, and four very familiar twentieth century friends.

Producer: Philippa Goodrich

A Juniper production for BBC Radio 4, first broadcast in September 2016.

Next Episode

8. The Cosmos

Does space go on for ever? Are there infinitely many stars?

These are some of the questions Adrian Moore explores in this episode in his series about philosophical thought concerning the infinite.

With the help of the theories of the Ancient Greeks through to those of modern cosmologists, Adrian examines the central question of whether our universe is finite or infinite.

For most of us, looking up at the stars gives us a sense of infinity but, as Adrian discovers, there is a strong body of opinion which suggests that space is finite, albeit unbounded. This is a difficult idea to grasp, but by inviting us to think of ourselves as ants, astrophysics professor Jo Dunkley attempts to explain it.

Adrian also tackles the idea of the expanding universe and the logic that leads cosmologists to argue that it all started with a big bang, and may all end with a big crunch.

Finally, we discover from cosmologist John Barrow how the appearance of an infinity in scientists’ calculations sends them straight back to the drawing board. The infinite, which the Ancient Greeks found so troubling, has lost none of its power to disturb.

Producer: Philippa Goodrich

A Juniper production for BBC Radio 4, first broadcast in September 2016.